Try subtracting 5 from both sides of $5 - 2x > 11$ and simplify what you get.

Once you have $-2x$ on one side, you will divide by $-2$. Remember what you must do to the inequality sign when you multiply or divide both sides by a negative number.

After dividing, you will have a fraction like $\frac{6}{-2}$. Simplify this to a single integer to write the final inequality.

In Desmos, enter y = 5 - 2x on one line and y = 11 on another. You will see a slanted line and a horizontal line.

Click where the two graphs intersect to see the intersection’s coordinates. The x-coordinate of this point is the value where $5 - 2x$ equals $11$.

Look at the graph to see for which x-values the line y = 5 - 2x is above the horizontal line y = 11 (since the inequality is $5 - 2x > 11$). From this region, write an inequality of the form $x$ (less than or greater than) that x-coordinate from the intersection.

Start with the inequality:

Subtract 5 from both sides to move the constant term:

which simplifies to:

Now divide both sides by $-2$ to solve for $x$.

Because you are dividing by a negative number, you must flip the inequality sign:

Simplify the right side:

From the previous step, you get the solution:

So the inequality that represents the solution set is $x < -3$, which corresponds to choice C.